A sample of 1497 carbon stars in the Large Magellanic Cloud (LMC) has been observed in the red part of the spectrum with the 2dF facility on the Anglo-Australian Telescope. Of these, 156 have been identified as J-type (i.e. ^13^C-rich) carbon stars using a technique which provides a clear distinction between J stars and the normal N-type carbon stars that comprise the bulk of the sample, and yields few borderline cases. A simple two-dimensional classification of the spectra, based on their spectral slopes in different wavelength regions, has been constructed and found to be related to the more conventional c and j indices, modified to suit the spectral regions observed. Most of the J stars form a photometric sequence in the K-(J-K) colour-magnitude diagram, parallel to and 0.6mag fainter than the N-star sequence. A subset of the J stars (about 13 per cent) are brighter than this J-star sequence; most of these are spectroscopically different from the other J stars. The bright J stars have stronger CN bands than the other J stars and are found strongly concentrated in the central regions of the LMC. Most of the rather few stars in common with Hartwick and Cowley's sample (1988ApJ...334..135H) of suspected CH stars are J stars. Overall, the proportion of carbon stars identified as J stars is somewhat lower than has been found in the Galaxy. The Na D lines are weaker in the LMC J stars than in either the Galactic J stars or the LMC N stars, and do not seem to depend on temperature.